Formal ontology of space, time, and physical entities in classical mechanics

2018 ◽  
Vol 13 (2) ◽  
pp. 135-179 ◽  
Author(s):  
Thomas Bittner
Keyword(s):  
Classical Mechanics ◽  
Space Time ◽  
Formal Ontology

Classical mechanics of special relativity in a Riemannian space‐time

1991 ◽  
Vol 32 (7) ◽  
pp. 1788-1795 ◽  
Author(s):  
Daniel Zerzion ◽  
L. P. Horwitz ◽  
R. I. Arshansky
Keyword(s):  
Special Relativity ◽  
Riemannian Space ◽  
Classical Mechanics ◽  
Space Time

scholarly journals Non-inertial frames in Minkowski space-time, accelerated either mathematical or dynamical observers and comments on non-inertial relativistic quantum mechanics

2014 ◽  
Vol 11 (10) ◽  
pp. 1450086 ◽  
Author(s):  
Horace W. Crater ◽  
Luca Lusanna
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Minkowski Space Time ◽  
Accelerated Observers ◽  
Inertial Frames ◽  
Locality Principle

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and how to define Unruh–DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.

Stochastic space-time and the concept of potential in classical mechanics

1980 ◽  
Vol 22 (10) ◽  
pp. 2384-2386 ◽  
Author(s):  
R. K. Roy Choudhury ◽  
S. Roy
Keyword(s):  
Classical Mechanics ◽  
Space Time ◽  
Stochastic Space

Classical mechanics in Galilean space-time

1981 ◽  
Vol 11 (9-10) ◽  
pp. 679-697 ◽  
Author(s):  
Ray E. Artz
Keyword(s):  
Classical Mechanics ◽  
Space Time ◽  
Galilean Space

scholarly journals Everything as an Algorithm ~ Computational Analysis and Model for Space/Time Complexity

2021 ◽  
Author(s):  
Andrew Kamal
Keyword(s):  
Subject Matter ◽  
Time Complexity ◽  
Quantum Physics ◽  
Computational Analysis ◽  
Classical Mechanics ◽  
Space Time ◽  
Quantum Similarity ◽  
The Subject ◽  
Origin Point

Utilizing multiple theorems derived from and formulating the equation : Z = {∀Θ ∈ Z → ∃s ∈ P S ∧ ∃t ∈ T : Θ = (s, t)} and formulating the equation: X = O + Ĥ + (n(log)Φ Pd x ), as well as some mathematical constraints and numerous implications in Quantum Physics, Classical Mechanics, and Algorithmic Quantization, we come up with a framework for mathematically representing our universe. These series of individualized papers make up a huge part of a dissertation on the subject matter of Quantum Similarity. Everything including how we view time itself and the origin point for our universe is explained in theoretical details throughout these papers.

scholarly journals Complex Covariance

10.14311/1809 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Frieder Kleefeld
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
Special Relativity ◽  
Degrees Of Freedom ◽  
Classical Mechanics ◽  
Space Time ◽  
Complex Phase ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Complex Valued

According to some generalized correspondence principle the classical limit of a non-Hermitian quantum theory describing quantum degrees of freedom is expected to be the well known classical mechanics of classical degrees of freedom in the complex phase space, i.e., some phase space spanned by complex-valued space and momentum coordinates. As special relativity was developed by Einstein merely for real-valued space-time and four-momentum, we will try to understand how special relativity and covariance can be extended to complex-valued space-time and four-momentum. Our considerations will lead us not only to some unconventional derivation of Lorentz transformations for complex-valued velocities, but also to the non-Hermitian Klein-Gordon and Dirac equations, which are to lay the foundations of a non-Hermitian quantum theory.

Force and energy in gravitational field

2021 ◽  
Vol 34 (1) ◽  
pp. 28-34
Author(s):  
Yan Yi
Keyword(s):  
Gravitational Field ◽  
Classical Mechanics ◽  
Inertial Force ◽  
Space Time ◽  
Reference Object ◽  
Mass Energy ◽  
Time Relationship ◽  
Basic Law ◽  
New Space ◽  
Object Relative

This is the second paper of the induction theory of gravitational field. In the first paper, a new space-time view, which considers the influence of gravity, was constructed. In the new view of time and space, classical mechanics no longer holds. In this paper, the theory of mechanics and energy is established in the new space-time relation. In this paper, the basic mechanical law in the new space-time relationship is derived from the inertial force of the observed object relative to the reference object. Second, according to this basic law, the new formulas of gravitation and electromagnetic force in the space-time relationship are derived. Third, the influence of the moving of the observation object on the force is discussed. Finally, the new law of mass energy conversion is discussed.

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